Does the type of armor matter? I know that Power Armor has a negative impact on stealth but I haven't really found anything substantial about other armors. Will I be detected more often when wearing metal armor than leather?
Your ability to sneak is directly effected by the weight of the armor you're wearing.
In most cases, it would be better to have lighter armor equipped.
If you have at least rank 4 in the Science! perk, you can modify your power armor chest with a stealth boy. This greatly increases the stealth capabilities, and would likely outweigh the stealth benefits of wearing lighter armor.
Currently the stealth boy for the Power Armor does show only when you are staying still. However the stealth boy for normal use shows you invisible when you're moving. However the description of the stealth boy power armor upgrade simply says that it activates a stealth field when crouched, so... It is currently unknown if this is a bug or not.
P.S. While the third person view does show you visible when moving while crouched in power armor, its possible that this is only a visual bug and either more extensive testing is required, or people will know for sure when the Creation Kit comes out.